details

property	value
status	complete
benchmark	MYNAT_nokinds_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n002.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.329102993011 seconds
cpu usage	0.326519253
max memory	1.3389824E7

stage attributes

key	value
output-size	17001
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o U11 : [o * o] --> o U21 : [o * o * o] --> o U31 : [o] --> o U41 : [o * o * o] --> o activate : [o] --> o and : [o * o] --> o isNat : [o] --> o n!6220!62200 : [] --> o n!6220!6220isNat : [o] --> o n!6220!6220plus : [o * o] --> o n!6220!6220s : [o] --> o n!6220!6220x : [o * o] --> o plus : [o * o] --> o s : [o] --> o tt : [] --> o x : [o * o] --> o U11(tt, X) => activate(X) U21(tt, X, Y) => s(plus(activate(Y), activate(X))) U31(tt) => 0 U41(tt, X, Y) => plus(x(activate(Y), activate(X)), activate(Y)) and(tt, X) => activate(X) isNat(n!6220!62200) => tt isNat(n!6220!6220plus(X, Y)) => and(isNat(activate(X)), n!6220!6220isNat(activate(Y))) isNat(n!6220!6220s(X)) => isNat(activate(X)) isNat(n!6220!6220x(X, Y)) => and(isNat(activate(X)), n!6220!6220isNat(activate(Y))) plus(X, 0) => U11(isNat(X), X) plus(X, s(Y)) => U21(and(isNat(Y), n!6220!6220isNat(X)), Y, X) x(X, 0) => U31(isNat(X)) x(X, s(Y)) => U41(and(isNat(Y), n!6220!6220isNat(X)), Y, X) 0 => n!6220!62200 plus(X, Y) => n!6220!6220plus(X, Y) isNat(X) => n!6220!6220isNat(X) s(X) => n!6220!6220s(X) x(X, Y) => n!6220!6220x(X, Y) activate(n!6220!62200) => 0 activate(n!6220!6220plus(X, Y)) => plus(activate(X), activate(Y)) activate(n!6220!6220isNat(X)) => isNat(X) activate(n!6220!6220s(X)) => s(activate(X)) activate(n!6220!6220x(X, Y)) => x(activate(X), activate(Y)) activate(X) => X We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): U11(tt, X) >? activate(X) U21(tt, X, Y) >? s(plus(activate(Y), activate(X))) U31(tt) >? 0 U41(tt, X, Y) >? plus(x(activate(Y), activate(X)), activate(Y)) and(tt, X) >? activate(X) isNat(n!6220!62200) >? tt isNat(n!6220!6220plus(X, Y)) >? and(isNat(activate(X)), n!6220!6220isNat(activate(Y))) isNat(n!6220!6220s(X)) >? isNat(activate(X)) isNat(n!6220!6220x(X, Y)) >? and(isNat(activate(X)), n!6220!6220isNat(activate(Y))) plus(X, 0) >? U11(isNat(X), X) plus(X, s(Y)) >? U21(and(isNat(Y), n!6220!6220isNat(X)), Y, X) x(X, 0) >? U31(isNat(X)) x(X, s(Y)) >? U41(and(isNat(Y), n!6220!6220isNat(X)), Y, X) 0 >? n!6220!62200 plus(X, Y) >? n!6220!6220plus(X, Y) isNat(X) >? n!6220!6220isNat(X) s(X) >? n!6220!6220s(X) x(X, Y) >? n!6220!6220x(X, Y) activate(n!6220!62200) >? 0 activate(n!6220!6220plus(X, Y)) >? plus(activate(X), activate(Y)) activate(n!6220!6220isNat(X)) >? isNat(X) activate(n!6220!6220s(X)) >? s(activate(X)) activate(n!6220!6220x(X, Y)) >? x(activate(X), activate(Y)) activate(X) >? X about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[U21(x_1, x_2, x_3)]] = U21(x_3, x_2, x_1) [[U41(x_1, x_2, x_3)]] = U41(x_3, x_2, x_1) [[activate(x_1)]] = x_1 [[tt]] = _|_ We choose Lex = {U21, U41, n!6220!6220plus, n!6220!6220x, plus, x} and Mul = {0, U11, U31, and, isNat, n!6220!62200, n!6220!6220isNat, n!6220!6220s, s}, and the following precedence: U41 = n!6220!6220x = x > U31 > 0 = n!6220!62200 > U21 = n!6220!6220plus = plus > isNat = n!6220!6220isNat = n!6220!6220s = s > U11 > and Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: U11(_|_, X) >= X U21(_|_, X, Y) > s(plus(Y, X)) popout

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